From: Liubov Dmitrieva <liubov.dmitrieva@gmail.com>
Date: Tue, 25 Sep 2012 18:44:46 +0000 (+0200)
Subject: Add optimized sincosf for SSE2 for x86 and x86-64
X-Git-Tag: upstream/2.30~10262
X-Git-Url: http://review.tizen.org/git/?a=commitdiff_plain;h=22bf5c179315edd33b8399102ea3cfbf92b4807f;p=external%2Fglibc.git

Add optimized sincosf for SSE2 for x86 and x86-64
---

diff --git a/ChangeLog b/ChangeLog
index 2a6e038..9a5ee9d 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,6 +1,18 @@
 2012-09-25  Liubov Dmitrieva  <liubov.dmitrieva@gmail.com>
 
-	* math/s_ccoshf.c (__ccoshf): Fix wrong using of sincosf for
+	* sysdeps/i386/i686/fpu/multiarch/Makefile (sysdep_routines):
+	Add s_sincosf-sse2.
+	* sysdeps/i386/i686/fpu/multiarch/s_sincosf.c: New file.
+	* sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S: New file.
+	* sysdeps/ieee754/flt-32/s_sincosf.c (SINCOSF, SINCOSF_FUNC): Add
+	macros for using routine as __sincosf_ia32.
+	Use macro for function declaration and weak_alias.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+
+	* sysdeps/x86_64/fpu/s_sincosf.S: New file.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Update.
+
+	* math/s_ccoshf.c (__ccoshf): Fix wrong usage of sincos for
 	subnormal argument.
 	* math/s_cexpf.c (__cexpf): Likewise.
 	* math/s_csinf.c (__csinf): Likewise.
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index d35635c..71b633a 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1490,9 +1490,9 @@ float: 1
 ifloat: 1
 Test "Real part of: cpow (0.75 + 1.25 i, 1.0 + 1.0 i) == 0.0846958290317209430433805274189191353 + 0.513285749182902449043287190519090481 i":
 double: 2
-float: 3
+float: 4
 idouble: 2
-ifloat: 3
+ifloat: 4
 ildouble: 3
 ldouble: 3
 Test "Imaginary part of: cpow (0.75 + 1.25 i, 1.0 + 1.0 i) == 0.0846958290317209430433805274189191353 + 0.513285749182902449043287190519090481 i":
@@ -1704,6 +1704,8 @@ ldouble: 1
 
 # ctan
 Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
 ildouble: 1
@@ -1797,6 +1799,8 @@ Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) ==
 ildouble: 1
 ldouble: 1
 Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
@@ -1827,9 +1831,9 @@ ildouble: 2
 ldouble: 2
 Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
@@ -1940,6 +1944,8 @@ ifloat: 3
 ildouble: 4
 ldouble: 4
 Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
+float: 1
+ifloat: 1
 ildouble: 1
 ldouble: 1
 
@@ -1954,9 +1960,9 @@ ildouble: 1
 ldouble: 1
 Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 1
 ldouble: 1
 Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i":
@@ -2564,9 +2570,6 @@ Test "sincos (0x1.fffff8p+127, &sin_res, &cos_res) puts 4.8578606313048733970111
 float: 1
 Test "sincos (0x1p+127, &sin_res, &cos_res) puts 6.23385512955870240370428801097126489001833e-01 in sin_res":
 float: 1
-Test "sincos (0x1p+50, &sin_res, &cos_res) puts 8.68095904660550604334592502063501320395739e-01 in cos_res":
-float: 1
-ifloat: 1
 Test "sincos (0x1p65, &sin_res, &cos_res) puts -0.047183876212354673805106149805700013943218 in sin_res":
 float: 1
 ifloat: 1
@@ -3442,6 +3445,8 @@ ildouble: 1
 ldouble: 1
 
 Function: Real part of "ctan_towardzero":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
 ildouble: 1
@@ -3461,9 +3466,9 @@ ldouble: 2
 
 Function: Imaginary part of "ctan_upward":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 4
 ldouble: 4
 
@@ -3514,6 +3519,8 @@ ildouble: 4
 ldouble: 4
 
 Function: Imaginary part of "ctanh_towardzero":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
 ildouble: 1
@@ -3521,9 +3528,9 @@ ldouble: 1
 
 Function: Real part of "ctanh_upward":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 4
 ldouble: 4
 
diff --git a/sysdeps/i386/i686/fpu/multiarch/Makefile b/sysdeps/i386/i686/fpu/multiarch/Makefile
index aa28f72..7d90892 100644
--- a/sysdeps/i386/i686/fpu/multiarch/Makefile
+++ b/sysdeps/i386/i686/fpu/multiarch/Makefile
@@ -1,3 +1,4 @@
 ifeq ($(subdir),math)
-libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2
+libm-sysdep_routines += e_expf-sse2 e_expf-ia32 s_sinf-sse2 s_cosf-sse2 \
+                        s_sincosf-sse2
 endif
diff --git a/sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S b/sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S
new file mode 100644
index 0000000..622f07a
--- /dev/null
+++ b/sysdeps/i386/i686/fpu/multiarch/s_sincosf-sse2.S
@@ -0,0 +1,586 @@
+/* Optimized with sse2 version of sincosf
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <sysdep.h>
+#define __need_Emath
+#include <bits/errno.h>
+
+/* Short algorithm description:
+ *
+ *  1) if |x|==0:    sin(x)=x,
+ *                   cos(x)=1.
+ *  2) if |x|<2^-27: sin(x)=x-x*DP_SMALL, raising underflow only when needed,
+ *                   cos(x)=1-|x|.
+ *  3) if |x|<2^-5 : sin(x)=x+x*x^2*DP_SIN2_0+x^5*DP_SIN2_1,
+ *                   cos(x)=1+1*x^2*DP_COS2_0+x^5*DP_COS2_1
+ *  4) if |x|< Pi/4: sin(x)=x+x*x^2*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))),
+ *                   cos(x)=1+1*x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).
+ *  5) if |x| < 9*Pi/4:
+ *      5.1) Range reduction:
+ *          k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, t=|x|-j*Pi/4.
+ *      5.2) Reconstruction:
+ *          sign_sin = sign(x) * (-1.0)^(( n   >>2)&1)
+ *          sign_cos =           (-1.0)^(((n+2)>>2)&1)
+ *          poly_sin = ((((S4*t^2 + S3)*t^2 + S2)*t^2 + S1)*t^2 + S0)*t^2*t+t
+ *          poly_cos = ((((C4*t^2 + C3)*t^2 + C2)*t^2 + C1)*t^2 + C0)*t^2*s+s
+ *          if(n&2 != 0) {
+ *              using cos(t) and sin(t) polynomials for |t|<Pi/4, results are
+ *              cos(x) = poly_sin * sign_cos
+ *              sin(x) = poly_cos * sign_sin
+ *          } else {
+ *              sin(x) = poly_sin * sign_sin
+ *              cos(x) = poly_cos * sign_cos
+ *          }
+ *  6) if |x| < 2^23, large args:
+ *      6.1) Range reduction:
+ *          k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4
+ *      6.2) Reconstruction same as (5.2).
+ *  7) if |x| >= 2^23, very large args:
+ *      7.1) Range reduction:
+ *          k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4.
+ *      7.2) Reconstruction same as (5.2).
+ *  8) if x is Inf, return x-x, and set errno=EDOM.
+ *  9) if x is NaN, return x-x.
+ *
+ * Special cases:
+ *  sin/cos(+-0) = +-0/1 not raising inexact/underflow,
+ *  sin/cos(subnormal) raises inexact/underflow,
+ *  sin/cos(min_normalized) raises inexact/underflow,
+ *  sin/cos(normalized) raises inexact,
+ *  sin/cos(Inf) = NaN, raises invalid, sets errno to EDOM,
+ *  sin/cos(NaN) = NaN.
+ */
+
+#ifdef	PIC
+# define MO1(symbol)			L(symbol)##@GOTOFF(%ebx)
+# define MO2(symbol,reg2,_scale)	L(symbol)##@GOTOFF(%ebx,reg2,_scale)
+# define CFI_PUSH(REG)	cfi_adjust_cfa_offset(4); cfi_rel_offset(REG,0)
+# define CFI_POP(REG)	cfi_adjust_cfa_offset(-4); cfi_restore(REG)
+# define PUSH(REG)			pushl REG; CFI_PUSH(REG)
+# define POP(REG)			popl REG; CFI_POP(REG)
+# define ENTRANCE			PUSH(%ebx); LOAD_PIC_REG(bx)
+# define RETURN				POP(%ebx); ret; CFI_PUSH(%ebx)
+# define ARG_X				8(%esp)
+# define ARG_SIN_PTR			12(%esp)
+# define ARG_COS_PTR			16(%esp)
+#else
+# define MO1(symbol)			L(symbol)
+# define MO2(symbol,reg2,_scale)	L(symbol)(,reg2,_scale)
+# define ENTRANCE
+# define RETURN				ret
+# define ARG_X				4(%esp)
+# define ARG_SIN_PTR			8(%esp)
+# define ARG_COS_PTR			12(%esp)
+#endif
+
+	.text
+ENTRY(__sincosf_sse2)
+	/* Input: single precision x on stack at address ARG_X */
+	/*        pointer to sin result on stack at address ARG_SIN_PTR */
+	/*        pointer to cos result on stack at address ARG_COS_PTR */
+
+	ENTRANCE
+	movl	ARG_X, %eax		/* Bits of x */
+	cvtss2sd ARG_X, %xmm0		/* DP x */
+	andl	$0x7fffffff, %eax	/* |x| */
+
+	cmpl	$0x3f490fdb, %eax	/* |x|<Pi/4 ? */
+	jb	L(arg_less_pio4)
+
+	/* Here if |x|>=Pi/4 */
+	movd	%eax, %xmm3		/* SP |x| */
+	andpd	MO1(DP_ABS_MASK),%xmm0	/* DP |x| */
+	movss	MO1(SP_INVPIO4), %xmm2	/* SP 1/(Pi/4) */
+
+	cmpl	$0x40e231d6, %eax	/* |x|<9*Pi/4 ? */
+	jae	L(large_args)
+
+	/* Here if Pi/4<=|x|<9*Pi/4 */
+	mulss	%xmm3, %xmm2		/* SP |x|/(Pi/4) */
+	movl	ARG_X, %ecx		/* Load x */
+	cvttss2si %xmm2, %eax		/* k, number of Pi/4 in x */
+	shrl	$29, %ecx		/* (sign of x) << 2 */
+	addl	$1, %eax		/* k+1 */
+	movl	$0x0e, %edx
+	andl	%eax, %edx		/* j = (k+1)&0x0e */
+	subsd	MO2(PIO4J,%edx,8), %xmm0/* t = |x| - j * Pi/4 */
+
+L(reconstruction):
+	/* Input: %eax=n, %xmm0=t, %ecx=sign(x) */
+
+	movaps	%xmm0, %xmm4		/* t */
+	movhpd	MO1(DP_ONES), %xmm4	/* 1|t */
+	mulsd	%xmm0, %xmm0		/* y=t^2 */
+	movl	$2, %edx
+	unpcklpd %xmm0, %xmm0		/* y|y */
+	addl	%eax, %edx		/* k+2 */
+	movaps	%xmm0, %xmm1		/* y|y */
+	mulpd	%xmm0, %xmm0		/* z=t^4|z=t^4 */
+
+	movaps	MO1(DP_SC4), %xmm2	/* S4 */
+	mulpd	%xmm0, %xmm2		/* z*S4 */
+	movaps	MO1(DP_SC3), %xmm3	/* S3 */
+	mulpd	%xmm0, %xmm3		/* z*S3 */
+	xorl	%eax, %ecx		/* (sign_x ^ (k>>2))<<2 */
+	addpd	MO1(DP_SC2), %xmm2	/* S2+z*S4 */
+	mulpd	%xmm0, %xmm2		/* z*(S2+z*S4) */
+	shrl	$2, %edx		/* (k+2)>>2 */
+	addpd	MO1(DP_SC1), %xmm3	/* S1+z*S3 */
+	mulpd	%xmm0, %xmm3		/* z*(S1+z*S3) */
+	shrl	$2, %ecx		/* sign_x ^ k>>2 */
+	addpd	MO1(DP_SC0), %xmm2	/* S0+z*(S2+z*S4) */
+	andl	$1, %edx		/* sign_cos = ((k+2)>>2)&1 */
+	mulpd	%xmm1, %xmm2		/* y*(S0+z*(S2+z*S4)) */
+	andl	$1, %ecx		/* sign_sin = sign_x ^ ((k>>2)&1) */
+	addpd	%xmm2, %xmm3		/* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */
+	mulpd	%xmm4, %xmm3		/*t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
+	testl	$2, %eax		/* n&2 != 0 ? */
+	addpd	%xmm4, %xmm3		/*t+t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
+	jnz	L(sin_result_sin_poly)
+
+/*L(sin_result_cos_poly):*/
+	/*
+	 * Here if
+	 * cos(x) = poly_sin * sign_cos
+	 * sin(x) = poly_cos * sign_sin
+	 */
+	movsd	MO2(DP_ONES,%ecx,8), %xmm4/* 0|sign_sin */
+	movhpd	MO2(DP_ONES,%edx,8), %xmm4/* sign_cos|sign_sin */
+	mulpd	%xmm4, %xmm3		/* result_cos|result_sin */
+	movl	ARG_SIN_PTR, %eax
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movl	ARG_COS_PTR, %ecx
+	movss	%xmm0, (%eax)		/* store sin(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move cos(x) to xmm0[0] */
+	movss	%xmm0, (%ecx)		/* store cos(x) */
+	RETURN
+
+	.p2align	4
+L(sin_result_sin_poly):
+	/*
+	 * Here if
+	 * sin(x) = poly_sin * sign_sin
+	 * cos(x) = poly_cos * sign_cos
+	 */
+	movsd	MO2(DP_ONES,%edx,8), %xmm4/* 0|sign_cos */
+	movhpd	MO2(DP_ONES,%ecx,8), %xmm4/* sign_sin|sign_cos */
+	mulpd	%xmm4, %xmm3		/* result_sin|result_cos */
+	movl	ARG_SIN_PTR, %eax
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movl	ARG_COS_PTR, %ecx
+	movss	%xmm0, (%ecx)		/* store cos(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move sin(x) to xmm0[0] */
+	movss	%xmm0, (%eax)		/* store sin(x) */
+	RETURN
+
+	.p2align	4
+L(large_args):
+	/* Here if |x|>=9*Pi/4 */
+	cmpl	$0x7f800000, %eax	/* x is Inf or NaN ? */
+	jae	L(arg_inf_or_nan)
+
+	/* Here if finite |x|>=9*Pi/4 */
+	cmpl	$0x4b000000, %eax	/* |x|<2^23 ? */
+	jae	L(very_large_args)
+
+	/* Here if 9*Pi/4<=|x|<2^23 */
+	movsd	MO1(DP_INVPIO4), %xmm1	/* 1/(Pi/4) */
+	mulsd	%xmm0, %xmm1		/* |x|/(Pi/4) */
+	cvttsd2si %xmm1, %eax		/* k=trunc(|x|/(Pi/4)) */
+	addl	$1, %eax		/* k+1 */
+	movl	%eax, %edx
+	andl	$0xfffffffe, %edx	/* j=(k+1)&0xfffffffe */
+	cvtsi2sdl %edx, %xmm4		/* DP j */
+	movl	ARG_X, %ecx		/* Load x */
+	movsd	MO1(DP_PIO4HI), %xmm2	/* -PIO4HI = high part of -Pi/4 */
+	shrl	$29, %ecx		/* (sign of x) << 2 */
+	mulsd	%xmm4, %xmm2		/* -j*PIO4HI */
+	movsd	MO1(DP_PIO4LO), %xmm3	/* -PIO4LO = low part of -Pi/4 */
+	addsd	%xmm2, %xmm0		/* |x| - j*PIO4HI */
+	mulsd	%xmm3, %xmm4		/* j*PIO4LO */
+	addsd	%xmm4, %xmm0		/* t = |x| - j*PIO4HI - j*PIO4LO */
+	jmp	L(reconstruction)
+
+	.p2align	4
+L(very_large_args):
+	/* Here if finite |x|>=2^23 */
+
+	/* bitpos = (ix>>23) - BIAS_32 + 59; */
+	shrl	$23, %eax		/* eb = biased exponent of x */
+	subl	$68, %eax		/* bitpos=eb-0x7f+59, where 0x7f */
+							/*is exponent bias */
+	movl	$28, %ecx		/* %cl=28 */
+	movl	%eax, %edx		/* bitpos copy */
+
+	/* j = bitpos/28; */
+	div	%cl			/* j in register %al=%ax/%cl */
+	movapd	%xmm0, %xmm3		/* |x| */
+	andl	$0xff, %eax		/* clear unneeded remainder from %ah*/
+
+	imull	$28, %eax, %ecx		/* j*28 */
+	movsd	MO1(DP_HI_MASK), %xmm4	/* DP_HI_MASK */
+	movapd	%xmm0, %xmm5		/* |x| */
+	mulsd	-2*8+MO2(_FPI,%eax,8), %xmm3/* tmp3 = FPI[j-2]*|x| */
+	movapd	%xmm0, %xmm1		/* |x| */
+	mulsd	-1*8+MO2(_FPI,%eax,8), %xmm5/* tmp2 = FPI[j-1]*|x| */
+	mulsd	0*8+MO2(_FPI,%eax,8), %xmm0/* tmp0 = FPI[j]*|x| */
+	addl	$19, %ecx		/* j*28+19 */
+	mulsd	1*8+MO2(_FPI,%eax,8), %xmm1/* tmp1 = FPI[j+1]*|x| */
+	cmpl	%ecx, %edx		/* bitpos>=j*28+19 ? */
+	jl	L(very_large_skip1)
+
+	/* Here if bitpos>=j*28+19 */
+	andpd	%xmm3, %xmm4		/* HI(tmp3) */
+	subsd	%xmm4, %xmm3		/* tmp3 = tmp3 - HI(tmp3) */
+L(very_large_skip1):
+
+	movsd	MO1(DP_2POW52), %xmm6
+	movapd	%xmm5, %xmm2		/* tmp2 copy */
+	addsd	%xmm3, %xmm5		/* tmp5 = tmp3 + tmp2 */
+	movl	$1, %edx
+	addsd	%xmm5, %xmm6		/* tmp6 = tmp5 + 2^52 */
+	movsd	8+MO1(DP_2POW52), %xmm4
+	movd	%xmm6, %eax		/* k = I64_LO(tmp6); */
+	addsd	%xmm6, %xmm4		/* tmp4 = tmp6 - 2^52 */
+	movl	ARG_X, %ecx		/* Load x */
+	comisd	%xmm5, %xmm4		/* tmp4 > tmp5 ? */
+	jbe	L(very_large_skip2)
+
+	/* Here if tmp4 > tmp5 */
+	subl	$1, %eax		/* k-- */
+	addsd	8+MO1(DP_ONES), %xmm4	/* tmp4 -= 1.0 */
+L(very_large_skip2):
+
+	andl	%eax, %edx		/* k&1 */
+	subsd	%xmm4, %xmm3		/* tmp3 -= tmp4 */
+	addsd	MO2(DP_ZERONE,%edx,8), %xmm3/* t  = DP_ZERONE[k&1] + tmp3 */
+	addsd	%xmm2, %xmm3		/* t += tmp2 */
+	shrl	$29, %ecx		/* (sign of x) << 2 */
+	addsd	%xmm3, %xmm0		/* t += tmp0 */
+	addl	$1, %eax		/* n=k+1 */
+	addsd	%xmm1, %xmm0		/* t += tmp1 */
+	mulsd	MO1(DP_PIO4), %xmm0	/* t *= PI04 */
+
+	jmp	L(reconstruction)	/* end of very_large_args peth */
+
+	.p2align	4
+L(arg_less_pio4):
+	/* Here if |x|<Pi/4 */
+	cmpl	$0x3d000000, %eax	/* |x|<2^-5 ? */
+	jl	L(arg_less_2pn5)
+
+	/* Here if 2^-5<=|x|<Pi/4 */
+	movaps	%xmm0, %xmm3		/* DP x */
+	movhpd	MO1(DP_ONES), %xmm3	/* DP 1|x */
+	mulsd	%xmm0, %xmm0		/* DP y=x^2 */
+	unpcklpd %xmm0, %xmm0		/* DP y|y */
+	movaps	%xmm0, %xmm1		/* y|y */
+	mulpd	%xmm0, %xmm0		/* z=x^4|z=x^4 */
+
+	movapd	MO1(DP_SC4), %xmm4	/* S4 */
+	mulpd	%xmm0, %xmm4		/* z*S4 */
+	movapd	MO1(DP_SC3), %xmm5	/* S3 */
+	mulpd	%xmm0, %xmm5		/* z*S3 */
+	addpd	MO1(DP_SC2), %xmm4	/* S2+z*S4 */
+	mulpd	%xmm0, %xmm4		/* z*(S2+z*S4) */
+	addpd	MO1(DP_SC1), %xmm5	/* S1+z*S3 */
+	mulpd	%xmm0, %xmm5		/* z*(S1+z*S3) */
+	addpd	MO1(DP_SC0), %xmm4	/* S0+z*(S2+z*S4) */
+	mulpd	%xmm1, %xmm4		/* y*(S0+z*(S2+z*S4)) */
+	mulpd	%xmm3, %xmm5		/* x*z*(S1+z*S3) */
+	mulpd	%xmm3, %xmm4		/* x*y*(S0+z*(S2+z*S4)) */
+	addpd	%xmm5, %xmm4		/*x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
+	movl	ARG_SIN_PTR, %eax
+	addpd	%xmm4, %xmm3		/*x+x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
+	movl	ARG_COS_PTR, %ecx
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movss	%xmm0, (%eax)		/* store sin(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move cos(x) to xmm0[0] */
+	movss	%xmm0, (%ecx)		/* store cos(x) */
+	RETURN
+
+	.p2align	4
+L(arg_less_2pn5):
+	/* Here if |x|<2^-5 */
+	cmpl	$0x32000000, %eax	/* |x|<2^-27 ? */
+	jl	L(arg_less_2pn27)
+
+	/* Here if 2^-27<=|x|<2^-5 */
+	movaps	%xmm0, %xmm1		/* DP x */
+	movhpd	MO1(DP_ONES), %xmm1	/* DP 1|x */
+	mulsd	%xmm0, %xmm0		/* DP x^2 */
+	unpcklpd %xmm0, %xmm0		/* DP x^2|x^2 */
+
+	movaps	MO1(DP_SINCOS2_1), %xmm3/* DP DP_SIN2_1 */
+	mulpd	%xmm0, %xmm3		/* DP x^2*DP_SIN2_1 */
+	addpd	MO1(DP_SINCOS2_0), %xmm3/* DP DP_SIN2_0+x^2*DP_SIN2_1 */
+	mulpd	%xmm0, %xmm3		/* DP x^2*DP_SIN2_0+x^4*DP_SIN2_1 */
+	mulpd	%xmm1, %xmm3		/* DP x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
+	addpd	%xmm1, %xmm3		/* DP x+x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
+	movl	ARG_SIN_PTR, %eax
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movl	ARG_COS_PTR, %ecx
+	movss	%xmm0, (%eax)		/* store sin(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move cos(x) to xmm0[0] */
+	movss	%xmm0, (%ecx)		/* store cos(x) */
+	RETURN
+
+	.p2align	4
+L(arg_less_2pn27):
+	movss	ARG_X, %xmm7		/* SP x */
+	cmpl	$0, %eax		/* x=0 ? */
+	je	L(arg_zero)		/* in case x=0 return sin(+-0)==+-0 */
+	/* Here if |x|<2^-27 */
+	/*
+	 * Special cases here:
+	 *  sin(subnormal) raises inexact/underflow
+	 *  sin(min_normalized) raises inexact/underflow
+	 *  sin(normalized) raises inexact
+	 *  cos(here)=1-|x| (raising inexact)
+	 */
+	movaps	%xmm0, %xmm3		/* DP x */
+	mulsd	MO1(DP_SMALL), %xmm0	/* DP x*DP_SMALL */
+	subsd	%xmm0, %xmm3		/* DP sin result is x-x*DP_SMALL */
+	andps	MO1(SP_ABS_MASK), %xmm7	/* SP |x| */
+	cvtsd2ss %xmm3, %xmm0		/* sin(x) */
+	movl	ARG_SIN_PTR, %eax
+	movss	MO1(SP_ONE), %xmm1	/* SP 1.0 */
+	movss	%xmm0, (%eax)		/* sin(x) store */
+	movl	ARG_COS_PTR, %ecx
+	subss	%xmm7, %xmm1		/* cos(x) */
+	movss	%xmm1, (%ecx)		/* cos(x) store */
+	RETURN
+
+	.p2align	4
+L(arg_zero):
+	movss	MO1(SP_ONE), %xmm0	/* 1.0 */
+	movl	ARG_SIN_PTR, %eax
+	movl	ARG_COS_PTR, %ecx
+	movss	%xmm7, (%eax)		/* sin(+-0)==x */
+	movss	%xmm0, (%ecx)		/* cos(+-0)==1 */
+	RETURN
+
+	.p2align	4
+L(arg_inf_or_nan):
+	movss	ARG_X, %xmm7		/* SP x */
+	/* Here if |x| is Inf or NAN */
+	jne	L(skip_errno_setting)	/* in case of x is NaN */
+
+	/* Here if x is Inf. Set errno to EDOM.  */
+	call	JUMPTARGET(__errno_location)
+	movl	$EDOM, (%eax)
+
+	.p2align	4
+L(skip_errno_setting):
+	/* Here if |x| is Inf or NAN. Continued. */
+	subss	%xmm7, %xmm7		/* x-x, result is NaN */
+	movl	ARG_SIN_PTR, %eax
+	movl	ARG_COS_PTR, %ecx
+	movss	%xmm7, (%eax)
+	movss	%xmm7, (%ecx)
+	RETURN
+END(__sincosf_sse2)
+
+	.section .rodata, "a"
+	.p2align 3
+L(PIO4J): /* Table of j*Pi/4, for j=0,1,..,10 */
+	.long	0x00000000,0x00000000
+	.long	0x54442d18,0x3fe921fb
+	.long	0x54442d18,0x3ff921fb
+	.long	0x7f3321d2,0x4002d97c
+	.long	0x54442d18,0x400921fb
+	.long	0x2955385e,0x400f6a7a
+	.long	0x7f3321d2,0x4012d97c
+	.long	0xe9bba775,0x4015fdbb
+	.long	0x54442d18,0x401921fb
+	.long	0xbeccb2bb,0x401c463a
+	.long	0x2955385e,0x401f6a7a
+	.type L(PIO4J), @object
+	ASM_SIZE_DIRECTIVE(L(PIO4J))
+
+	.p2align 3
+L(_FPI): /* 4/Pi broken into sum of positive DP values */
+	.long	0x00000000,0x00000000
+	.long	0x6c000000,0x3ff45f30
+	.long	0x2a000000,0x3e3c9c88
+	.long	0xa8000000,0x3c54fe13
+	.long	0xd0000000,0x3aaf47d4
+	.long	0x6c000000,0x38fbb81b
+	.long	0xe0000000,0x3714acc9
+	.long	0x7c000000,0x3560e410
+	.long	0x56000000,0x33bca2c7
+	.long	0xac000000,0x31fbd778
+	.long	0xe0000000,0x300b7246
+	.long	0xe8000000,0x2e5d2126
+	.long	0x48000000,0x2c970032
+	.long	0xe8000000,0x2ad77504
+	.long	0xe0000000,0x290921cf
+	.long	0xb0000000,0x274deb1c
+	.long	0xe0000000,0x25829a73
+	.long	0xbe000000,0x23fd1046
+	.long	0x10000000,0x2224baed
+	.long	0x8e000000,0x20709d33
+	.long	0x80000000,0x1e535a2f
+	.long	0x64000000,0x1cef904e
+	.long	0x30000000,0x1b0d6398
+	.long	0x24000000,0x1964ce7d
+	.long	0x16000000,0x17b908bf
+	.type L(_FPI), @object
+	ASM_SIZE_DIRECTIVE(L(_FPI))
+
+/* Coefficients of polynomials for */
+/* sin(x)~=x+x*x^2*(DP_SIN2_0+x^2*DP_SIN2_1) in low  DP part, */
+/* cos(x)~=1+1*x^2*(DP_COS2_0+x^2*DP_COS2_1) in high DP part, */
+/* for |x|<2^-5. */
+	.p2align 4
+L(DP_SINCOS2_0):
+	.long	0x5543d49d,0xbfc55555
+	.long	0xff5cc6fd,0xbfdfffff
+	.type L(DP_SINCOS2_0), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_0))
+
+	.p2align 4
+L(DP_SINCOS2_1):
+	.long	0x75cec8c5,0x3f8110f4
+	.long	0xb178dac5,0x3fa55514
+	.type L(DP_SINCOS2_1), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_1))
+
+	.p2align 3
+L(DP_ZERONE):
+	.long	0x00000000,0x00000000	/* 0.0 */
+	.long	0x00000000,0xbff00000	/* 1.0 */
+	.type L(DP_ZERONE), @object
+	ASM_SIZE_DIRECTIVE(L(DP_ZERONE))
+
+	.p2align 3
+L(DP_ONES):
+	.long	0x00000000,0x3ff00000	/* +1.0 */
+	.long	0x00000000,0xbff00000	/* -1.0 */
+	.type L(DP_ONES), @object
+	ASM_SIZE_DIRECTIVE(L(DP_ONES))
+
+/* Coefficients of polynomials for */
+/* sin(t)~=t+t*t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4)))) in low  DP part, */
+/* cos(t)~=1+1*t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4)))) in high DP part, */
+/* for |t|<Pi/4. */
+	.p2align 4
+L(DP_SC4):
+	.long	0x1674b58a,0xbe5a947e
+	.long	0xdd8844d7,0xbe923c97
+	.type L(DP_SC4), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC4))
+
+	.p2align 4
+L(DP_SC3):
+	.long	0x64e6b5b4,0x3ec71d72
+	.long	0x9ac43cc0,0x3efa00eb
+	.type L(DP_SC3), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC3))
+
+	.p2align 4
+L(DP_SC2):
+	.long	0x8b4bd1f9,0xbf2a019f
+	.long	0x348b6874,0xbf56c16b
+	.type L(DP_SC2), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC2))
+
+	.p2align 4
+L(DP_SC1):
+	.long	0x10c2688b,0x3f811111
+	.long	0x545c50c7,0x3fa55555
+	.type L(DP_SC1), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC1))
+
+	.p2align 4
+L(DP_SC0):
+	.long	0x55551cd9,0xbfc55555
+	.long	0xfffe98ae,0xbfdfffff
+	.type L(DP_SC0), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC0))
+
+	.p2align 3
+L(DP_SMALL):
+	.long	0x00000000,0x3cd00000	/* 2^(-50) */
+	.type L(DP_SMALL), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SMALL))
+
+	.p2align 3
+L(DP_PIO4):
+	.long	0x54442d18,0x3fe921fb	/* Pi/4 */
+	.type L(DP_PIO4), @object
+	ASM_SIZE_DIRECTIVE(L(DP_PIO4))
+
+	.p2align 3
+L(DP_2POW52):
+	.long	0x00000000,0x43300000	/* +2^52 */
+	.long	0x00000000,0xc3300000	/* -2^52 */
+	.type L(DP_2POW52), @object
+	ASM_SIZE_DIRECTIVE(L(DP_2POW52))
+
+	.p2align 3
+L(DP_INVPIO4):
+	.long	0x6dc9c883,0x3ff45f30	/* 4/Pi */
+	.type L(DP_INVPIO4), @object
+	ASM_SIZE_DIRECTIVE(L(DP_INVPIO4))
+
+	.p2align 3
+L(DP_PIO4HI):
+	.long	0x54000000,0xbfe921fb	/* High part of Pi/4 */
+	.type L(DP_PIO4HI), @object
+	ASM_SIZE_DIRECTIVE(L(DP_PIO4HI))
+
+	.p2align 3
+L(DP_PIO4LO):
+	.long	0x11A62633,0xbe010b46	/* Low part of Pi/4 */
+	.type L(DP_PIO4LO), @object
+	ASM_SIZE_DIRECTIVE(L(DP_PIO4LO))
+
+	.p2align 2
+L(SP_INVPIO4):
+	.long	0x3fa2f983		/* 4/Pi */
+	.type L(SP_INVPIO4), @object
+	ASM_SIZE_DIRECTIVE(L(SP_INVPIO4))
+
+	.p2align 4
+L(DP_ABS_MASK): /* Mask for getting DP absolute value */
+	.long	0xffffffff,0x7fffffff
+	.long	0xffffffff,0x7fffffff
+	.type L(DP_ABS_MASK), @object
+	ASM_SIZE_DIRECTIVE(L(DP_ABS_MASK))
+
+	.p2align 3
+L(DP_HI_MASK): /* Mask for getting high 21 bits of DP value */
+	.long	0x00000000,0xffffffff
+	.type L(DP_HI_MASK), @object
+	ASM_SIZE_DIRECTIVE(L(DP_HI_MASK))
+
+	.p2align 4
+L(SP_ABS_MASK): /* Mask for getting SP absolute value */
+	.long	0x7fffffff,0x7fffffff
+	.long	0x7fffffff,0x7fffffff
+	.type L(SP_ABS_MASK), @object
+	ASM_SIZE_DIRECTIVE(L(SP_ABS_MASK))
+
+	.p2align 2
+L(SP_ONE):
+	.long	0x3f800000		/* 1.0 */
+	.type L(SP_ONE), @object
+	ASM_SIZE_DIRECTIVE(L(SP_ONE))
+
+weak_alias(__sincosf, sincosf)
diff --git a/sysdeps/i386/i686/fpu/multiarch/s_sincosf.c b/sysdeps/i386/i686/fpu/multiarch/s_sincosf.c
new file mode 100644
index 0000000..c5e856a
--- /dev/null
+++ b/sysdeps/i386/i686/fpu/multiarch/s_sincosf.c
@@ -0,0 +1,29 @@
+/* Multiple versions of sincosf
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <init-arch.h>
+
+extern void __sincosf_sse2 (float, float *, float *);
+extern void __sincosf_ia32 (float, float *, float *);
+void __sincosf (float, float *, float *);
+
+libm_ifunc (__sincosf, HAS_SSE2 ? __sincosf_sse2 : __sincosf_ia32);
+weak_alias (__sincosf, sincosf);
+
+#define SINCOSF __sincosf_ia32
+#include <sysdeps/ieee754/flt-32/s_sincosf.c>
diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c
index 1b4d000..c3bd998 100644
--- a/sysdeps/ieee754/flt-32/s_sincosf.c
+++ b/sysdeps/ieee754/flt-32/s_sincosf.c
@@ -21,9 +21,14 @@
 
 #include <math_private.h>
 
+#ifndef SINCOSF
+# define SINCOSF_FUNC __sincosf
+#else
+# define SINCOSF_FUNC SINCOSF
+#endif
 
 void
-__sincosf (float x, float *sinx, float *cosx)
+SINCOSF_FUNC (float x, float *sinx, float *cosx)
 {
   int32_t ix;
 
@@ -70,4 +75,7 @@ __sincosf (float x, float *sinx, float *cosx)
 	}
     }
 }
+
+#ifndef SINCOSF
 weak_alias (__sincosf, sincosf)
+#endif
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index b02b9e6..d79578c 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1579,6 +1579,9 @@ ildouble: 1
 ldouble: 1
 
 # ctan
+Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 1
+ifloat: 1
 Test "Real part of: ctan (-2 - 3 i) == 0.376402564150424829275122113032269084e-2 - 1.00323862735360980144635859782192726 i":
 double: 1
 float: 1
@@ -1612,6 +1615,8 @@ Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.225462792499754505792678258
 ildouble: 1
 ldouble: 1
 Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i":
+float: 2
+ifloat: 2
 double: 1
 idouble: 1
 Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i":
@@ -1757,6 +1762,8 @@ idouble: 1
 ildouble: 1
 ldouble: 1
 Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 2
+ifloat: 2
 double: 1
 idouble: 1
 Test "Imaginary part of: ctanh (45 + 1 i) == 1.000000000000000000000000000000000000001 + 1.490158918874345552942703234806348520895e-39 i":
@@ -1765,6 +1772,9 @@ ldouble: 1
 Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i":
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i":
+float: 1
+ifloat: 1
 
 # ctanh_downward
 Test "Real part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i":
@@ -2399,8 +2409,8 @@ ifloat: 2
 ildouble: 1
 ldouble: 1
 Test "sin_upward (3) == 0.1411200080598672221007448028081102798469":
-float: 1
-ifloat: 1
+float: 2
+ifloat: 2
 ildouble: 1
 ldouble: 1
 Test "sin_upward (4) == -0.7568024953079282513726390945118290941359":
@@ -2430,12 +2440,6 @@ ifloat: 1
 Test "sincos (0.80190127184058835, &sin_res, &cos_res) puts 0.69534156199418473 in cos_res":
 double: 1
 idouble: 1
-Test "sincos (0x1p+120, &sin_res, &cos_res) puts -9.25879022854837867303861764107414946730833e-01 in cos_res":
-float: 1
-ifloat: 1
-Test "sincos (0x1p+127, &sin_res, &cos_res) puts 7.81914638714960072263910298466369236613162e-01 in cos_res":
-float: 1
-ifloat: 1
 Test "sincos (M_PI_6l*2.0, &sin_res, &cos_res) puts 0.5 in cos_res":
 double: 1
 float: 1
@@ -2705,6 +2709,8 @@ Test "y1 (0x1.001000001p+593) == 3.927269966354206207832593635798954916263e-90":
 ildouble: 2
 ldouble: 2
 Test "y1 (0x1.27e204p+99) == -8.881610148467797208469612080785210013461e-16":
+float: 1
+ifloat: 1
 double: 1
 idouble: 1
 ildouble: 1
@@ -3085,8 +3091,8 @@ ildouble: 1
 ldouble: 1
 
 Function: "cos_upward":
-float: 1
-ifloat: 1
+float: 2
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
@@ -3174,17 +3180,17 @@ ldouble: 1
 
 Function: Real part of "ctan":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 2
 ldouble: 2
 
 Function: Imaginary part of "ctan":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
@@ -3242,9 +3248,9 @@ ldouble: 4
 
 Function: Real part of "ctanh":
 double: 1
-float: 1
+float: 2
 idouble: 1
-ifloat: 1
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
@@ -3445,8 +3451,8 @@ ildouble: 1
 ldouble: 1
 
 Function: "sin_upward":
-float: 1
-ifloat: 1
+float: 2
+ifloat: 2
 ildouble: 1
 ldouble: 1
 
diff --git a/sysdeps/x86_64/fpu/s_sincosf.S b/sysdeps/x86_64/fpu/s_sincosf.S
new file mode 100644
index 0000000..3334a3a
--- /dev/null
+++ b/sysdeps/x86_64/fpu/s_sincosf.S
@@ -0,0 +1,558 @@
+/* Optimized sincosf function.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <sysdep.h>
+#define __need_Emath
+#include <bits/errno.h>
+
+/* Short algorithm description:
+ *
+ *  1) if |x|==0:    sin(x)=x,
+ *                   cos(x)=1.
+ *  2) if |x|<2^-27: sin(x)=x-x*DP_SMALL, raising underflow only when needed,
+ *                   cos(x)=1-|x|.
+ *  3) if |x|<2^-5 : sin(x)=x+x*x^2*DP_SIN2_0+x^5*DP_SIN2_1,
+ *                   cos(x)=1+1*x^2*DP_COS2_0+x^5*DP_COS2_1
+ *  4) if |x|< Pi/4: sin(x)=x+x*x^2*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))),
+ *                   cos(x)=1+1*x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))).
+ *  5) if |x| < 9*Pi/4:
+ *      5.1) Range reduction:
+ *          k=trunc(|x|/(Pi/4)), j=(k+1)&0x0e, n=k+1, t=|x|-j*Pi/4.
+ *      5.2) Reconstruction:
+ *          sign_sin = sign(x) * (-1.0)^(( n   >>2)&1)
+ *          sign_cos =           (-1.0)^(((n+2)>>2)&1)
+ *          poly_sin = ((((S4*t^2 + S3)*t^2 + S2)*t^2 + S1)*t^2 + S0)*t^2*t+t
+ *          poly_cos = ((((C4*t^2 + C3)*t^2 + C2)*t^2 + C1)*t^2 + C0)*t^2*s+s
+ *          if(n&2 != 0) {
+ *              using cos(t) and sin(t) polynomials for |t|<Pi/4, results are
+ *              cos(x) = poly_sin * sign_cos
+ *              sin(x) = poly_cos * sign_sin
+ *          } else {
+ *              sin(x) = poly_sin * sign_sin
+ *              cos(x) = poly_cos * sign_cos
+ *          }
+ *  6) if |x| < 2^23, large args:
+ *      6.1) Range reduction:
+ *          k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4
+ *      6.2) Reconstruction same as (5.2).
+ *  7) if |x| >= 2^23, very large args:
+ *      7.1) Range reduction:
+ *          k=trunc(|x|/(Pi/4)), j=(k+1)&0xfffffffe, n=k+1, t=|x|-j*Pi/4.
+ *      7.2) Reconstruction same as (5.2).
+ *  8) if x is Inf, return x-x, and set errno=EDOM.
+ *  9) if x is NaN, return x-x.
+ *
+ * Special cases:
+ *  sin/cos(+-0) = +-0/1 not raising inexact/underflow,
+ *  sin/cos(subnormal) raises inexact/underflow,
+ *  sin/cos(min_normalized) raises inexact/underflow,
+ *  sin/cos(normalized) raises inexact,
+ *  sin/cos(Inf) = NaN, raises invalid, sets errno to EDOM,
+ *  sin/cos(NaN) = NaN.
+ */
+
+# define ARG_SIN_PTR	%rdi
+# define ARG_COS_PTR	%rsi
+
+	.text
+ENTRY(__sincosf)
+	/* Input: %xmm0 contains single precision argument x */
+	/*        %rdi points to sin result */
+	/*        %rsi points to cos result */
+
+	movd	%xmm0, %eax		/* Bits of x */
+	movaps	%xmm0, %xmm7		/* Copy of x */
+	cvtss2sd %xmm0, %xmm0		/* DP x */
+	movss	L(SP_ABS_MASK)(%rip), %xmm3
+	movl	%eax, %r8d		/* Copy of x bits */
+	andl	$0x7fffffff, %eax	/* |x| */
+
+	cmpl	$0x3f490fdb, %eax	/* |x|<Pi/4 ? */
+	jb	L(arg_less_pio4)
+
+	/* Here if |x|>=Pi/4 */
+	andps	%xmm7, %xmm3		/* SP |x| */
+	andpd	L(DP_ABS_MASK)(%rip),%xmm0 /* DP |x| */
+	movss	L(SP_INVPIO4)(%rip), %xmm2 /* SP 1/(Pi/4) */
+
+	cmpl	$0x40e231d6, %eax	/* |x|<9*Pi/4 ? */
+	jae	L(large_args)
+
+	/* Here if Pi/4<=|x|<9*Pi/4 */
+	mulss	%xmm3, %xmm2		/* SP |x|/(Pi/4) */
+	movl	%r8d, %ecx		/* Load x */
+	cvttss2si %xmm2, %eax		/* k, number of Pi/4 in x */
+	lea	L(PIO4J)(%rip), %r9
+	shrl	$29, %ecx		/* (sign of x) << 2 */
+	addl	$1, %eax		/* k+1 */
+	movl	$0x0e, %edx
+	andl	%eax, %edx		/* j = (k+1)&0x0e */
+	subsd	(%r9,%rdx,8), %xmm0	/* t = |x| - j * Pi/4 */
+
+L(reconstruction):
+	/* Input: %eax=n, %xmm0=t, %ecx=sign(x) */
+
+	movaps	%xmm0, %xmm4		/* t */
+	movhpd	L(DP_ONES)(%rip), %xmm4 /* 1|t */
+	mulsd	%xmm0, %xmm0		/* y=t^2 */
+	movl	$2, %edx
+	unpcklpd %xmm0, %xmm0		/* y|y */
+	addl	%eax, %edx		/* k+2 */
+	movaps	%xmm0, %xmm1		/* y|y */
+	mulpd	%xmm0, %xmm0		/* z=t^4|z=t^4 */
+
+	movaps	L(DP_SC4)(%rip), %xmm2	/* S4 */
+	mulpd	%xmm0, %xmm2		/* z*S4 */
+	movaps	L(DP_SC3)(%rip), %xmm3	/* S3 */
+	mulpd	%xmm0, %xmm3		/* z*S3 */
+	xorl	%eax, %ecx		/* (sign_x ^ (k>>2))<<2 */
+	addpd	L(DP_SC2)(%rip), %xmm2	/* S2+z*S4 */
+	mulpd	%xmm0, %xmm2		/* z*(S2+z*S4) */
+	shrl	$2, %edx		/* (k+2)>>2 */
+	addpd	L(DP_SC1)(%rip), %xmm3	/* S1+z*S3 */
+	mulpd	%xmm0, %xmm3		/* z*(S1+z*S3) */
+	shrl	$2, %ecx		/* sign_x ^ k>>2 */
+	addpd	L(DP_SC0)(%rip), %xmm2	/* S0+z*(S2+z*S4) */
+	andl	$1, %edx		/* sign_cos = ((k+2)>>2)&1 */
+	mulpd	%xmm1, %xmm2		/* y*(S0+z*(S2+z*S4)) */
+	andl	$1, %ecx		/* sign_sin = sign_x ^ ((k>>2)&1) */
+	addpd	%xmm2, %xmm3		/* y*(S0+y*(S1+y*(S2+y*(S3+y*S4)))) */
+	lea	L(DP_ONES)(%rip), %r9
+	mulpd	%xmm4, %xmm3		/*t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
+	testl	$2, %eax		/* n&2 != 0 ? */
+	addpd	%xmm4, %xmm3		/*t+t*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
+	jnz	L(sin_result_sin_poly)
+
+/*L(sin_result_cos_poly):*/
+	/*
+	 * Here if
+	 * cos(x) = poly_sin * sign_cos
+	 * sin(x) = poly_cos * sign_sin
+	 */
+	movsd	(%r9,%rcx,8), %xmm4	/* 0|sign_sin */
+	movhpd	(%r9,%rdx,8), %xmm4	/* sign_cos|sign_sin */
+	mulpd	%xmm4, %xmm3		/* result_cos|result_sin */
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movss	%xmm0, (ARG_SIN_PTR)	/* store sin(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move cos(x) to xmm0[0] */
+	movss	%xmm0, (ARG_COS_PTR)	/* store cos(x) */
+	ret
+
+	.p2align	4
+L(sin_result_sin_poly):
+	/*
+	 * Here if
+	 * sin(x) = poly_sin * sign_sin
+	 * cos(x) = poly_cos * sign_cos
+	 */
+	movsd	(%r9,%rdx,8), %xmm4	/* 0|sign_cos */
+	movhpd	(%r9,%rcx,8), %xmm4	/* sign_sin|sign_cos */
+	mulpd	%xmm4, %xmm3		/* result_sin|result_cos */
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movss	%xmm0, (ARG_COS_PTR)	/* store cos(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move sin(x) to xmm0[0] */
+	movss	%xmm0, (ARG_SIN_PTR)	/* store sin(x) */
+	ret
+
+	.p2align	4
+L(large_args):
+	/* Here if |x|>=9*Pi/4 */
+	cmpl	$0x7f800000, %eax	/* x is Inf or NaN ? */
+	jae	L(arg_inf_or_nan)
+
+	/* Here if finite |x|>=9*Pi/4 */
+	cmpl	$0x4b000000, %eax	/* |x|<2^23 ? */
+	jae	L(very_large_args)
+
+	/* Here if 9*Pi/4<=|x|<2^23 */
+	movsd	L(DP_INVPIO4)(%rip), %xmm1 /* 1/(Pi/4) */
+	mulsd	%xmm0, %xmm1		/* |x|/(Pi/4) */
+	cvttsd2si %xmm1, %eax		/* k=trunc(|x|/(Pi/4)) */
+	addl	$1, %eax		/* k+1 */
+	movl	%eax, %edx
+	andl	$0xfffffffe, %edx	/* j=(k+1)&0xfffffffe */
+	cvtsi2sdl %edx, %xmm4		/* DP j */
+	movl	%r8d, %ecx		/* Load x */
+	movsd	L(DP_PIO4HI)(%rip), %xmm2 /* -PIO4HI = high part of -Pi/4 */
+	shrl	$29, %ecx		/* (sign of x) << 2 */
+	mulsd	%xmm4, %xmm2		/* -j*PIO4HI */
+	movsd	L(DP_PIO4LO)(%rip), %xmm3 /* -PIO4LO = low part of -Pi/4 */
+	addsd	%xmm2, %xmm0		/* |x| - j*PIO4HI */
+	mulsd	%xmm3, %xmm4		/* j*PIO4LO */
+	addsd	%xmm4, %xmm0		/* t = |x| - j*PIO4HI - j*PIO4LO */
+	jmp	L(reconstruction)
+
+	.p2align	4
+L(very_large_args):
+	/* Here if finite |x|>=2^23 */
+
+	/* bitpos = (ix>>23) - BIAS_32 + 59; */
+	shrl	$23, %eax		/* eb = biased exponent of x */
+	subl	$68, %eax		/* bitpos=eb-0x7f+59, where 0x7f */
+							/*is exponent bias */
+	movl	$28, %ecx		/* %cl=28 */
+	movl	%eax, %edx		/* bitpos copy */
+
+	/* j = bitpos/28; */
+	div	%cl			/* j in register %al=%ax/%cl */
+	movapd	%xmm0, %xmm3		/* |x| */
+	andl	$0xff, %eax		/* clear unneeded remainder from %ah*/
+
+	imull	$28, %eax, %ecx		/* j*28 */
+	lea	L(_FPI)(%rip), %r9
+	movsd	L(DP_HI_MASK)(%rip), %xmm4 /* DP_HI_MASK */
+	movapd	%xmm0, %xmm5		/* |x| */
+	mulsd	-16(%r9,%rax,8), %xmm3	/* tmp3 = FPI[j-2]*|x| */
+	movapd	%xmm0, %xmm1		/* |x| */
+	mulsd	-8(%r9,%rax,8), %xmm5	/* tmp2 = FPI[j-1]*|x| */
+	mulsd	(%r9,%rax,8), %xmm0	/* tmp0 = FPI[j]*|x| */
+	addl	$19, %ecx		/* j*28+19 */
+	mulsd	8(%r9,%rax,8), %xmm1	/* tmp1 = FPI[j+1]*|x| */
+	cmpl	%ecx, %edx		/* bitpos>=j*28+19 ? */
+	jl	L(very_large_skip1)
+
+	/* Here if bitpos>=j*28+19 */
+	andpd	%xmm3, %xmm4		/* HI(tmp3) */
+	subsd	%xmm4, %xmm3		/* tmp3 = tmp3 - HI(tmp3) */
+L(very_large_skip1):
+
+	movsd	L(DP_2POW52)(%rip), %xmm6
+	movapd	%xmm5, %xmm2		/* tmp2 copy */
+	addsd	%xmm3, %xmm5		/* tmp5 = tmp3 + tmp2 */
+	movl	$1, %edx
+	addsd	%xmm5, %xmm6		/* tmp6 = tmp5 + 2^52 */
+	movsd	8+L(DP_2POW52)(%rip), %xmm4
+	movd	%xmm6, %eax		/* k = I64_LO(tmp6); */
+	addsd	%xmm6, %xmm4		/* tmp4 = tmp6 - 2^52 */
+	movl	%r8d, %ecx		/* Load x */
+	comisd	%xmm5, %xmm4		/* tmp4 > tmp5 ? */
+	jbe	L(very_large_skip2)
+
+	/* Here if tmp4 > tmp5 */
+	subl	$1, %eax		/* k-- */
+	addsd	8+L(DP_ONES)(%rip), %xmm4 /* tmp4 -= 1.0 */
+L(very_large_skip2):
+
+	andl	%eax, %edx		/* k&1 */
+	lea	L(DP_ZERONE)(%rip), %r9
+	subsd	%xmm4, %xmm3		/* tmp3 -= tmp4 */
+	addsd	(%r9,%rdx,8), %xmm3	/* t  = DP_ZERONE[k&1] + tmp3 */
+	addsd	%xmm2, %xmm3		/* t += tmp2 */
+	shrl	$29, %ecx		/* (sign of x) << 2 */
+	addsd	%xmm3, %xmm0		/* t += tmp0 */
+	addl	$1, %eax		/* n=k+1 */
+	addsd	%xmm1, %xmm0		/* t += tmp1 */
+	mulsd	L(DP_PIO4)(%rip), %xmm0	/* t *= PI04 */
+
+	jmp	L(reconstruction)	/* end of very_large_args peth */
+
+	.p2align	4
+L(arg_less_pio4):
+	/* Here if |x|<Pi/4 */
+	cmpl	$0x3d000000, %eax	/* |x|<2^-5 ? */
+	jl	L(arg_less_2pn5)
+
+	/* Here if 2^-5<=|x|<Pi/4 */
+	movaps	%xmm0, %xmm3		/* DP x */
+	movhpd	L(DP_ONES)(%rip), %xmm3 /* DP 1|x */
+	mulsd	%xmm0, %xmm0		/* DP y=x^2 */
+	unpcklpd %xmm0, %xmm0		/* DP y|y */
+	movaps	%xmm0, %xmm1		/* y|y */
+	mulpd	%xmm0, %xmm0		/* z=x^4|z=x^4 */
+
+	movapd	L(DP_SC4)(%rip), %xmm4	/* S4 */
+	mulpd	%xmm0, %xmm4		/* z*S4 */
+	movapd	L(DP_SC3)(%rip), %xmm5	/* S3 */
+	mulpd	%xmm0, %xmm5		/* z*S3 */
+	addpd	L(DP_SC2)(%rip), %xmm4	/* S2+z*S4 */
+	mulpd	%xmm0, %xmm4		/* z*(S2+z*S4) */
+	addpd	L(DP_SC1)(%rip), %xmm5	/* S1+z*S3 */
+	mulpd	%xmm0, %xmm5		/* z*(S1+z*S3) */
+	addpd	L(DP_SC0)(%rip), %xmm4	/* S0+z*(S2+z*S4) */
+	mulpd	%xmm1, %xmm4		/* y*(S0+z*(S2+z*S4)) */
+	mulpd	%xmm3, %xmm5		/* x*z*(S1+z*S3) */
+	mulpd	%xmm3, %xmm4		/* x*y*(S0+z*(S2+z*S4)) */
+	addpd	%xmm5, %xmm4		/*x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))))*/
+	addpd	%xmm4, %xmm3		/*x+x*y*(S0+y*(S1+y*(S2+y*(S3+y*S4))*/
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movss	%xmm0, (ARG_SIN_PTR)	/* store sin(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move cos(x) to xmm0[0] */
+	movss	%xmm0, (ARG_COS_PTR)	/* store cos(x) */
+	ret
+
+	.p2align	4
+L(arg_less_2pn5):
+	/* Here if |x|<2^-5 */
+	cmpl	$0x32000000, %eax	/* |x|<2^-27 ? */
+	jl	L(arg_less_2pn27)
+
+	/* Here if 2^-27<=|x|<2^-5 */
+	movaps	%xmm0, %xmm1		/* DP x */
+	movhpd	L(DP_ONES)(%rip), %xmm1 /* DP 1|x */
+	mulsd	%xmm0, %xmm0		/* DP x^2 */
+	unpcklpd %xmm0, %xmm0		/* DP x^2|x^2 */
+
+	movaps	L(DP_SINCOS2_1)(%rip), %xmm3 /* DP DP_SIN2_1 */
+	mulpd	%xmm0, %xmm3		/* DP x^2*DP_SIN2_1 */
+	addpd	L(DP_SINCOS2_0)(%rip), %xmm3 /* DP DP_SIN2_0+x^2*DP_SIN2_1 */
+	mulpd	%xmm0, %xmm3		/* DP x^2*DP_SIN2_0+x^4*DP_SIN2_1 */
+	mulpd	%xmm1, %xmm3		/* DP x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
+	addpd	%xmm1, %xmm3		/* DP x+x^3*DP_SIN2_0+x^5*DP_SIN2_1 */
+	cvtpd2ps %xmm3, %xmm0		/* SP results */
+	movss	%xmm0, (ARG_SIN_PTR)	/* store sin(x) from xmm0[0] */
+	shufps	$1, %xmm0, %xmm0	/* move cos(x) to xmm0[0] */
+	movss	%xmm0, (ARG_COS_PTR)	/* store cos(x) */
+	ret
+
+	.p2align	4
+L(arg_less_2pn27):
+	cmpl	$0, %eax		/* x=0 ? */
+	je	L(arg_zero)		/* in case x=0 return sin(+-0)==+-0 */
+	/* Here if |x|<2^-27 */
+	/*
+	 * Special cases here:
+	 *  sin(subnormal) raises inexact/underflow
+	 *  sin(min_normalized) raises inexact/underflow
+	 *  sin(normalized) raises inexact
+	 *  cos(here)=1-|x| (raising inexact)
+	 */
+	movaps	%xmm0, %xmm3		/* DP x */
+	mulsd	L(DP_SMALL)(%rip), %xmm0/* DP x*DP_SMALL */
+	subsd	%xmm0, %xmm3		/* DP sin result is x-x*DP_SMALL */
+	andps	L(SP_ABS_MASK)(%rip), %xmm7/* SP |x| */
+	cvtsd2ss %xmm3, %xmm0		/* sin(x) */
+	movss	L(SP_ONE)(%rip), %xmm1	/* SP 1.0 */
+	movss	%xmm0, (ARG_SIN_PTR)	/* sin(x) store */
+	subss	%xmm7, %xmm1		/* cos(x) */
+	movss	%xmm1, (ARG_COS_PTR)	/* cos(x) store */
+	ret
+
+	.p2align	4
+L(arg_zero):
+	movss	L(SP_ONE)(%rip), %xmm0	/* 1.0 */
+	movss	%xmm7, (ARG_SIN_PTR)	/* sin(+-0)==x */
+	movss	%xmm0, (ARG_COS_PTR)	/* cos(+-0)==1 */
+	ret
+
+	.p2align	4
+L(arg_inf_or_nan):
+	/* Here if |x| is Inf or NAN */
+	jne	L(skip_errno_setting)	/* in case of x is NaN */
+
+	/* Here if x is Inf. Set errno to EDOM.  */
+	call	JUMPTARGET(__errno_location)
+	movl	$EDOM, (%rax)
+
+	.p2align	4
+L(skip_errno_setting):
+	/* Here if |x| is Inf or NAN. Continued. */
+	subss	%xmm7, %xmm7		/* x-x, result is NaN */
+	movss	%xmm7, (ARG_SIN_PTR)
+	movss	%xmm7, (ARG_COS_PTR)
+	ret
+END(__sincosf)
+
+	.section .rodata, "a"
+	.p2align 3
+L(PIO4J): /* Table of j*Pi/4, for j=0,1,..,10 */
+	.long	0x00000000,0x00000000
+	.long	0x54442d18,0x3fe921fb
+	.long	0x54442d18,0x3ff921fb
+	.long	0x7f3321d2,0x4002d97c
+	.long	0x54442d18,0x400921fb
+	.long	0x2955385e,0x400f6a7a
+	.long	0x7f3321d2,0x4012d97c
+	.long	0xe9bba775,0x4015fdbb
+	.long	0x54442d18,0x401921fb
+	.long	0xbeccb2bb,0x401c463a
+	.long	0x2955385e,0x401f6a7a
+	.type L(PIO4J), @object
+	ASM_SIZE_DIRECTIVE(L(PIO4J))
+
+	.p2align 3
+L(_FPI): /* 4/Pi broken into sum of positive DP values */
+	.long	0x00000000,0x00000000
+	.long	0x6c000000,0x3ff45f30
+	.long	0x2a000000,0x3e3c9c88
+	.long	0xa8000000,0x3c54fe13
+	.long	0xd0000000,0x3aaf47d4
+	.long	0x6c000000,0x38fbb81b
+	.long	0xe0000000,0x3714acc9
+	.long	0x7c000000,0x3560e410
+	.long	0x56000000,0x33bca2c7
+	.long	0xac000000,0x31fbd778
+	.long	0xe0000000,0x300b7246
+	.long	0xe8000000,0x2e5d2126
+	.long	0x48000000,0x2c970032
+	.long	0xe8000000,0x2ad77504
+	.long	0xe0000000,0x290921cf
+	.long	0xb0000000,0x274deb1c
+	.long	0xe0000000,0x25829a73
+	.long	0xbe000000,0x23fd1046
+	.long	0x10000000,0x2224baed
+	.long	0x8e000000,0x20709d33
+	.long	0x80000000,0x1e535a2f
+	.long	0x64000000,0x1cef904e
+	.long	0x30000000,0x1b0d6398
+	.long	0x24000000,0x1964ce7d
+	.long	0x16000000,0x17b908bf
+	.type L(_FPI), @object
+	ASM_SIZE_DIRECTIVE(L(_FPI))
+
+/* Coefficients of polynomials for */
+/* sin(x)~=x+x*x^2*(DP_SIN2_0+x^2*DP_SIN2_1) in low  DP part, */
+/* cos(x)~=1+1*x^2*(DP_COS2_0+x^2*DP_COS2_1) in high DP part, */
+/* for |x|<2^-5. */
+	.p2align 4
+L(DP_SINCOS2_0):
+	.long	0x5543d49d,0xbfc55555
+	.long	0xff5cc6fd,0xbfdfffff
+	.type L(DP_SINCOS2_0), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_0))
+
+	.p2align 4
+L(DP_SINCOS2_1):
+	.long	0x75cec8c5,0x3f8110f4
+	.long	0xb178dac5,0x3fa55514
+	.type L(DP_SINCOS2_1), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SINCOS2_1))
+
+
+	.p2align 3
+L(DP_ZERONE):
+	.long	0x00000000,0x00000000	/* 0.0 */
+	.long	0x00000000,0xbff00000	/* 1.0 */
+	.type L(DP_ZERONE), @object
+	ASM_SIZE_DIRECTIVE(L(DP_ZERONE))
+
+	.p2align 3
+L(DP_ONES):
+	.long	0x00000000,0x3ff00000	/* +1.0 */
+	.long	0x00000000,0xbff00000	/* -1.0 */
+	.type L(DP_ONES), @object
+	ASM_SIZE_DIRECTIVE(L(DP_ONES))
+
+/* Coefficients of polynomials for */
+/* sin(t)~=t+t*t^2*(S0+t^2*(S1+t^2*(S2+t^2*(S3+t^2*S4)))) in low  DP part, */
+/* cos(t)~=1+1*t^2*(C0+t^2*(C1+t^2*(C2+t^2*(C3+t^2*C4)))) in high DP part, */
+/* for |t|<Pi/4. */
+	.p2align 4
+L(DP_SC4):
+	.long	0x1674b58a,0xbe5a947e
+	.long	0xdd8844d7,0xbe923c97
+	.type L(DP_SC4), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC4))
+
+	.p2align 4
+L(DP_SC3):
+	.long	0x64e6b5b4,0x3ec71d72
+	.long	0x9ac43cc0,0x3efa00eb
+	.type L(DP_SC3), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC3))
+
+	.p2align 4
+L(DP_SC2):
+	.long	0x8b4bd1f9,0xbf2a019f
+	.long	0x348b6874,0xbf56c16b
+	.type L(DP_SC2), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC2))
+
+	.p2align 4
+L(DP_SC1):
+	.long	0x10c2688b,0x3f811111
+	.long	0x545c50c7,0x3fa55555
+	.type L(DP_SC1), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC1))
+
+	.p2align 4
+L(DP_SC0):
+	.long	0x55551cd9,0xbfc55555
+	.long	0xfffe98ae,0xbfdfffff
+	.type L(DP_SC0), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SC0))
+
+	.p2align 3
+L(DP_SMALL):
+	.long	0x00000000,0x3cd00000	/* 2^(-50) */
+	.type L(DP_SMALL), @object
+	ASM_SIZE_DIRECTIVE(L(DP_SMALL))
+
+	.p2align 3
+L(DP_PIO4):
+	.long	0x54442d18,0x3fe921fb	/* Pi/4 */
+	.type L(DP_PIO4), @object
+	ASM_SIZE_DIRECTIVE(L(DP_PIO4))
+
+	.p2align 3
+L(DP_2POW52):
+	.long	0x00000000,0x43300000	/* +2^52 */
+	.long	0x00000000,0xc3300000	/* -2^52 */
+	.type L(DP_2POW52), @object
+	ASM_SIZE_DIRECTIVE(L(DP_2POW52))
+
+	.p2align 3
+L(DP_INVPIO4):
+	.long	0x6dc9c883,0x3ff45f30	/* 4/Pi */
+	.type L(DP_INVPIO4), @object
+	ASM_SIZE_DIRECTIVE(L(DP_INVPIO4))
+
+	.p2align 3
+L(DP_PIO4HI):
+	.long	0x54000000,0xbfe921fb	/* High part of Pi/4 */
+	.type L(DP_PIO4HI), @object
+	ASM_SIZE_DIRECTIVE(L(DP_PIO4HI))
+
+	.p2align 3
+L(DP_PIO4LO):
+	.long	0x11A62633,0xbe010b46	/* Low part of Pi/4 */
+	.type L(DP_PIO4LO), @object
+	ASM_SIZE_DIRECTIVE(L(DP_PIO4LO))
+
+	.p2align 2
+L(SP_INVPIO4):
+	.long	0x3fa2f983		/* 4/Pi */
+	.type L(SP_INVPIO4), @object
+	ASM_SIZE_DIRECTIVE(L(SP_INVPIO4))
+
+	.p2align 4
+L(DP_ABS_MASK): /* Mask for getting DP absolute value */
+	.long	0xffffffff,0x7fffffff
+	.long	0xffffffff,0x7fffffff
+	.type L(DP_ABS_MASK), @object
+	ASM_SIZE_DIRECTIVE(L(DP_ABS_MASK))
+
+	.p2align 3
+L(DP_HI_MASK): /* Mask for getting high 21 bits of DP value */
+	.long	0x00000000,0xffffffff
+	.type L(DP_HI_MASK), @object
+	ASM_SIZE_DIRECTIVE(L(DP_HI_MASK))
+
+	.p2align 4
+L(SP_ABS_MASK): /* Mask for getting SP absolute value */
+	.long	0x7fffffff,0x7fffffff
+	.long	0x7fffffff,0x7fffffff
+	.type L(SP_ABS_MASK), @object
+	ASM_SIZE_DIRECTIVE(L(SP_ABS_MASK))
+
+	.p2align 2
+L(SP_ONE):
+	.long	0x3f800000		/* 1.0 */
+	.type L(SP_ONE), @object
+	ASM_SIZE_DIRECTIVE(L(SP_ONE))
+
+weak_alias(__sincosf, sincosf)